where \(\eta \)  is the fluid viscosity. The height \(u_{\rm c}\)  of the critical constriction can
be obtained using the Persson contact mechanics theory
(see Ref. [1]}, [2]}, [3]}, [4]}, [5]}). The result (1)
is for a seal with a square nominal contact area. For a rectangular contact area with the length
\(L_x\)  in the fluid flow direction and \(L_y\)  in the orthogonal direction, there will be an
additional factor \(L_y/L_x\)  in (1). In a typical case the seal has a circular (radius \(r_0\) )
cross section (like for rubber O-rings), and in this case \(L_y=2 \pi r_0\)  and typically \(L_y/L_x >> 1\)  in which case the
leak-rate will be much larger than given by the square-leak-rate formula (1). However, this
geometrical correction factor is trivially accounted for. In deriving (1) it is assumed that the fluid
pressure is negligible compared to the nominal contact pressure. If this is not the case one must include the
deformation of the elastic solids by the fluid pressure distribution[6]}.
